Quantum Key Distribution (QKD), based on the laws of quantum physics, can offer unconditional secure communication between two legitimate parties (Alice and Bob) [1]}, [2]}, [3]}, even if there exists a malicious eavesdropper (Eve). The first QKD protocol is proposed by Bennett and Brassard in 1984 named BB84 [4]}. Hereafter, it has attracted extensive attention and developed rapidly both in theory and experiment [5]}, [6]}, [7]}. The security proof of BB84 protocol with nonideal photon sources was given by Gottesman et al. [8]}, [9]}, and the decoy state method [10]}, [11]} was invented to counter attack the photon number splitting (PNS) attacks [12]}, corresponding experimental demonstrations were exhibited [13]}, [14]}, [15]}. Moreover, to solve those attacks directed on the detecting side, the measurement-device-independent quantum key distribution (MDI-QKD) protocol was put forward [16]}, [17]}. Combined with the decoy-state method, MDI-QKD has the ability of avoiding attacks aiming at detectors and multi-photon components in the light source. Thereafter, a larger number of theoretical and experimental works have been carried out to improve practical performances of MDI-QKD [18]}, [19]}, [20]}, [21]}, [22]}, [23]}.
